Quote by lawnmower man
planet A is traveling through time twice as fast as earth.

No. Planet A and Earth are moving at approx .9c with respect to each other. Each sees the other as moving slower by 50%. Both are right. Neither has a privileged point of view.
Quote by lawnmower man
Planet B is traveling through time at the same speed as earth.

B and Earth are at rest wrt each other.
Quote by lawnmower man
Planet C is traveling through time at half the speed of earth

C and Earth are moving at approx .9c with respect to each other. Each sees the other as moving slower by 50%. Both are right. Neither has a privileged point of view.
Quote by lawnmower man
on planet A anna runs a 4 minute mile with time travel at twice the speed as on earth
on planet B bob runs a 4 minute mile with time traveling at the same speed as on earth
on planet c clare runs a 4 minute mile with time traveling at half the speed as on earth
so if we now measure how fast each runner would had to of run to achieve a 4 minute mile using the time speed of planet Bs to measure all 3 then
anna would have to run at 7.5 miles per hour
bob would have to run at 15 miles per hour
clare would have to run at 30 mile per hour
so my question is? is this correct?

No. Dilation is never
experienced, it is only
observed. Each sees the
others as moving slower
( and always slower, never faster).